Tomographic readout of an opto-mechanical interferometer

TL;DR

This paper demonstrates a quantum state tomography technique for light reflected from a mechanical oscillator, achieving noise levels below the standard quantum limit using a homodyne detection setup.

Contribution

It introduces a method for complete quadrature readout of light interacting with a mechanical oscillator in an interferometer, surpassing the standard quantum limit.

Findings

Achieved a readout noise of 1.9 x 10^{-16} m/√Hz at 133 kHz.

Readout noise was dominated by shot noise, not technical noise.

Surpassed the standard quantum limit by a factor of 8.2 (9 dB).

Abstract

The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. The complete tomographic reconstruction of the state of light requires the ability to readout arbitrary quadratures. Here we demonstrate such a readout by applying a balanced homodyne detector to an interferometric position measurement of a thermally excited high-Q silicon nitride membrane in a Michelson-Sagnac interferometer. A readout noise of $\unit{1.9 \cdot 10^{-16}}{\metre/\sqrt{\hertz}}$ around the membrane's fundamental oscillation mode at $\unit{133}{\kilo\hertz}$ has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.